In the earliest decades of construction scheduling research, the emphasis was on methods such as the CPM, PERT, and linear/integer programming formulations. These approaches were valuable because they provided clear structure and transparency: given fixed precedence constraints and known durations, one could compute earliest/latest start times, slack, float, and total project duration. However, they were predicated on strong assumptions about resource availability and typically ignored or simplified resource constraints (especially when resources are shared, multi-mode, or variable over time). As the network size, number of tasks, and resource types grew, these deterministic methods began to struggle. In large construction networks, the computational burden of exact integer programming models became prohibitive; heuristics based on priority rules (e.g., longest processing time first, earliest finish time) offered faster solutions but often provided sub-optimal smoothing of resource usage.

In the context of resource levelling, specifically the goal of smoothing resource demand over time rather than just minimising makespan, heuristic approaches began to emerge. For example, resource-driven scheduling methods in repetitive construction (such as high-rise or pipeline work) were introduced to reduce idle time and maximise the continuity of crew or equipment deployment. These methods emphasised discipline in resource flow (keeping crews busy, avoiding resource peaks and troughs), but often relied on domain-specific rules rather than general optimisation frameworks [3].

As computational power increased and scheduling models became more complex (e.g., multi-mode tasks, renewable and non-renewable resources, stochastic durations), researchers shifted to metaheuristic approaches. These techniques, inspired by natural processes (evolution, swarm intelligence, annealing) or competitive models, are ideally suited to large combinatorial-search spaces, nondifferentiable objective functions, and multi-objective trade-offs.

For instance, a significant line of work developed in the mid-2010s explored metaheuristic methods for resource-leveling large-scale construction projects. One doctoral thesis was dedicated to the design of efficient heuristic and meta-heuristic methods for the Resource-Levelling Problem (RLP) and the Discrete Time-Cost Trade-Off Problems (DTCTP) in large construction scheduling contexts. It showed that hybrid methods (e.g., memetic algorithms combined with simulated annealing, or quasi-stable, schedule-focused GAs) outperformed simpler heuristic rules, particularly on significant problems that typical software tools struggled with.

Another study applied a GA specifically to resource levelling in construction projects, accounting for daily resource usage and aiming to minimise variability (the sum of squared deviations from a desired level). Results from sample projects indicated that GA could significantly reduce resource peaks and smooth the temporal distribution of workforce or equipment use compared to default scheduling tools [12].

Metaheuristic studies also addressed multi‐objective trade-offs in construction scheduling. For example, construction managers care not only about duration (makespan) but also cost, quality, resource utilization, and risk. An article considered the time-cost-quality trade-off in a bridge-project context, modelling both renewable and non-renewable resources and applying three metaheuristic algorithms (multi-objective grey wolf optimizer, NSGA-II, multi-objective PSO) to evaluate performance. That work underscored the flexibility of metaheuristics when traditional deterministic methods became intractable or overly restrictive [13].

In addition to model complexity, scalability became a key concern. One study on multi-project scheduling in construction (multiple overlapping projects sharing resources) introduced hybrid metaheuristics combining GA, simulated annealing, and backward-forward improvement heuristics, addressing the challenge of resource conflicts across projects (something classical CPM could not handle).

While makespan minimisation remains a core focus, many researchers recognised that for construction projects, resource levelling (i.e., smoothing peaks and troughs in resource usage) is equally vital for cost control, productivity, and stability. One study explored the RLP with a fixed project duration and the minimisation of resource usage fluctuations. The authors proposed greedy algorithms and hybrid low-level heuristics embedded within population-based metaheuristics (differential evolution, GA, PSO) and demonstrated that hybridisation yields smoother resource profiles [3].

Work on repetitive construction projects (e.g., multi-unit buildings, linear infrastructure) also emphasised the unique nature of resource allocation there: crews often move from unit to unit, resource continuity is critical, and variability can lead to high costs or delays. A study on multi-objective resource-constrained scheduling for large repetitive projects applied differential evolution to a project comprising 160 activities and 16 repetitive sub-projects, demonstrating that metaheuristics can scale beyond toy problems and approximate real-world complexity while addressing conflicting objectives (duration vs. usage stability) [8].

These developments illustrate that metaheuristics moved the field from “just finish as soon as possible” to “finish as soon as possible while using resources smoothly, cost-effectively, and with less waste/idle time.” However, most approaches still rely on selecting a single metaheuristic (or a fixed hybrid) and tailoring it to problem instances.

More recently, the field of scheduling and resource allocation has begun to embrace hyper-heuristics, which represent a higher‐level shift: rather than using a single algorithm, the idea is to manage, select, generate, or adapt multiple heuristics dynamically. A hyper-heuristic framework consists of a high-level controller and a pool of low-level heuristics/metaheuristics; the controller learns (or decides) which low-level algorithm to apply under which circumstances, ideally adapting to instance features or search progress.

In other domains (manufacturing, flow shop scheduling, cloud computing, vehicle routing), hyper-heuristic approaches have shown strong promise. For example, a Q-learning‐based hyper-heuristic was used to schedule tasks in a distributed flow shop environment with energy-efficiency objectives. The RL agent, selected based on makespan and energy consumption, exhibited superior convergence and robustness compared with fixed-heuristic selection strategies. Another study proposed a MAP-Elites–based hyper-heuristic for the Resource-Constrained Project Scheduling Problem (RCPSP) that maintained an archive of diverse heuristic behaviours and selected them based on performance diversity across instances [4], [5]. In the construction scheduling context, the adoption of hyper-heuristics is still relatively limited but emerging. Some work on construction resource-levelling has referenced hyper-heuristic frameworks, but predominantly in the generic scheduling literature rather than in construction-specific case studies. The need for dynamic algorithm selection is especially acute in construction because projects differ widely in scale, resource types, precedence complexity, merge‐split relationships, and duration uncertainty. A framework that can learn which heuristic strategy to apply and when, rather than relying on manual tuning, therefore holds great appeal [11].

Despite these advances, several key gaps remain in the literature and, hence, the opportunities your proposed WHH algorithm addresses.

First, while many metaheuristic studies target makespan or cost, fewer explicitly focus on resource levelling (smooth resource utilisation) as a structured objective alongside duration/cost. Those that do often assume a fixed algorithm or per-instance tuning, rather than a framework that adapts dynamically. Second, most past studies use a single heuristic/metaheuristic, or a fixed hybrid (e.g., GA combined with local search). What is lacking is a unified framework that embeds multiple heuristics and selects them adaptively at runtime. This is precisely the promise of hyper-heuristics, but construction‐specific adoption remains minimal [8].

Third, many studies are limited to small-to-medium-sized problems (e.g., 30-100 activities) or assume relatively simple resource/environmental structures. Real construction projects often involve multiple resource types, precedence networks, multi‐mode tasks, stochastic durations, and dynamic changes (material delays, workforce shifts). A generalized adaptive optimisation framework is therefore needed.

Fourth, parameter tuning remains a heavy burden. Metaheuristics often require careful adjustment of crossover/mutation rates, swarm velocities, pheromone evaporation rates, and related parameters. Static tuning may yield sub‐optimal performance when problem characteristics shift. A control mechanism that learns which algorithm works when mitigates this burden.

Finally, monitoring convergence and deciding when to switch strategies is rarely addressed in depth. A hyper-heuristic that monitors performance indicators (diversity, improvement rate, stagnation) in real time and switches heuristics accordingly is an area of active research, but not yet widespread in construction resource scheduling [1].

The proposed WHH algorithm sits at this nexus of opportunity. It brings together multiple underlying metaheuristics (GA, PSO, ACO, SA, ICA) under a reinforcement learning‐based controller that dynamically selects or blends the algorithms during the search. The WHH is designed to minimise not just project duration, but also explicit measures of resource fluctuation (e.g., moments of resource usage, distribution over time), and to adapt across different project instances without heavy retuning. In doing so, it addresses the fundamental shift from “one fixed algorithm per problem” to “a system of algorithms plus learning controller,” aligning with the hyper-heuristic vision but tailoring it to the construction resource allocation and levelling domain [2].

In short, the literature shows a clear evolution: deterministic scheduling → heuristics → metaheuristics → hyper-heuristics/learning‐based frameworks. However, in the specific niche of construction resource allocation and levelling, the last step (fully adaptive hyper‐heuristic frameworks) remains under-explored. The WHH fills that gap by offering a higher‐level, adaptive, generalisable optimisation framework, grounded in the traditional metaheuristic toolkit and forward‐looking in its learning control paradigm.

Construction project scheduling is fundamentally a balancing act between time, resources, and costs. Among these, resource allocation and levelling are among the most challenging optimization problems due to their nonlinear, discrete, and dynamic nature. Projects often involve multiple activities that compete for limited resources, such as labor, machinery, or materials, under strict precedence relationships and varying productivity rates. The goal is to determine how these resources should be assigned over time so that project objectives are met efficiently while maintaining stable resource usage throughout the project’s life cycle. In its most basic form, the RALP can be described as follows: given a set of project activities, each with a duration, resource demand, and precedence constraints, determine the start and finish times for each activity and allocate the available resources so that fluctuations in resource usage are minimized. In practice, this means keeping resource utilization as smooth as possible, avoiding sharp peaks (overloads) and valleys (idleness), while ensuring the project duration remains acceptable or minimal.

Formally, let there be activities in a construction project. Each activity requires a certain amount of resource ri for a given duration di, subject to precedence relationships Pij that defines the execution order between activities i and j. The total available resource at any time t is limited by a capacity Rmax. The objective is not only to complete all activities within the project horizon, but also to distribute the resource load over time to avoid significant fluctuations.

To capture the dynamics of resource usage, let R(t) denote the total amount of a specific resource used at time t. This is obtained by summing the demands of all activities active at that time. The average or mean resource utilization over the project’s time horizon T can be defined as

R ̅ = ∑ R(t).

This average serves as a benchmark for what constitutes “perfectly smooth” usage, though in real projects, such smoothness is rarely achievable due to task interdependencies and precedence constraints. The degree of unevenness or fluctuation in resource utilization can then be quantified through two principal indices. The first, Mx, represents the total variation or fluctuation around the average resource usage:

Mx = ∑(R(t) − R ) .

This formulation is conceptually similar to variance; it penalizes deviations (both upward and downward) from the mean utilization level. A smaller value of Mx indicates smoother resource consumption, implying that resource demand over time is more consistent and predictable. Minimizing Mx helps managers avoid resource bottlenecks, reduce idle times, and maintain stable crew deployment, which ultimately leads to lower indirect costs and improved productivity. The second measure, My, captures the distribution of resource utilization over time. It is defined as

M = ∑[t. (R(t) − R ̅ )].

Unlike Mx, which focuses on the magnitude of fluctuations, My accounts for when these fluctuations occur. In effect, it measures the temporal balance of resource usage. A low value of My implies that the project maintains a relatively balanced distribution of resources across the early and late stages, avoiding front-loading (high usage at the beginning) or back-loading (peaks near the project end). This is particularly important for large-scale projects where resources must be shared across multiple sites or phases.

Together, Mx and My provide complementary perspectives on resource stability: the first measures smoothness, while the second assesses symmetry in utilization over time. Achieving optimal levelling means minimizing both indices concurrently, which naturally leads to a multi-objective optimization problem. The comprehensive objective function for the RALP can thus be formulated as

Minimize:f = w1. Project Duration + w2. Mx + w3. My, where w1, w2, and w3 are non-negative weight coefficients representing the relative importance assigned to each objective: duration, fluctuation, and temporal balance. The inclusion of weights allows flexible prioritization depending on project conditions. For instance, in a fast-track project where deadlines are critical, w1 may dominate, while in projects with stable schedules but a limited workforce, w2 and w3 may be emphasized.

This multi-objective structure reflects real-world trade-offs faced by construction managers. Shorter durations typically require greater resource intensity, increasing fluctuations and costs. Conversely, achieving a perfectly levelled resource profile often implies extended project durations or lower productivity. The optimization challenge lies in balancing these competing objectives.

The optimization problem is subject to several practical and technical constraints, which ensure the feasibility and realism of the resulting schedule.

The multi-objective formulation captures several fundamental trade-offs:

Duration vs. fluctuation: reducing project duration often requires mobilizing more resources simultaneously, creating usage peaks. Conversely, strict levelling constraints tend to elongate the project.

Smoothness vs symmetry: minimizing Mx may yield smooth usage but not necessarily balanced over time. For example, one could have constant high usage early on, followed by idleness, which would still score well on Mx but poorly on My. Balancing both ensures steady demand across the timeline.

Cost implications: fluctuating resource usage typically increases indirect costs due to hiring/firing cycles, idle equipment, and logistical inefficiencies. A well-levelled schedule can therefore indirectly minimize cost even if not explicitly included in the objective.

From a managerial perspective, these objectives mirror practical goals: ensuring continuity of work crews, minimizing mobilization/demobilization cycles, reducing downtime, and enhancing predictability of resource consumption for procurement and subcontracting.

The solution space of the RALP grows exponentially with the number of activities. Even for moderate-sized projects (50–100 tasks), the number of feasible schedules can be astronomical. Several factors contribute to this complexity:

I. Combinatorial explosion: every possible permutation of activity start times that respects precedence creates a unique schedule. The combinatorial nature makes exhaustive enumeration impossible.

II. Discrete resource profiles: since activity start times are discrete (e.g., in days), the resource usage function R(t) changes in discrete steps, producing a rugged objective landscape with many local minima.

III. Non-linearity of objective functions: the square term in Mx and time-weighted deviations in My create nonlinear relationships between start times and overall objective value.

IV. Conflict between objectives: The three objectives are interdependent and often conflict with one another.

Improvements in one may worsen another, requiring trade-off exploration using Pareto optimization or weighted aggregation.

V. Dynamic uncertainty: In real projects, durations and resource availabilities are stochastic. Hence, a robust solution must remain effective under variable conditions.

These challenges justify the use of metaheuristic and hyper-heuristic approaches. Unlike deterministic algorithms, metaheuristics such as GA, PSO, or ACO can navigate complex landscapes through global and local exploration, and are easily adapted to multi-objective contexts. A hyper-heuristic system, like the proposed WHH, adds another layer of intelligence by learning which metaheuristic is most effective at different stages of search, thereby enhancing convergence speed and solution diversity.

In practical project management, resource levelling is not merely a mathematical exercise; it has direct consequences for performance, cost, and morale. A poorly levelled schedule can lead to overstaffing during some periods and idleness during others, resulting in budget overruns, demotivation, and logistical inefficiencies. Consistent resource demand, by contrast, enables better workforce planning, stable subcontractor engagement, and smoother supply-chain operations.

Furthermore, levelling aligns closely with the lean construction concept, which aims to minimize waste and variability. Smooth resource usage means fewer disruptions, less material waste, and more predictable output rates, all contributing to leaner, more sustainable projects. Modern construction firms are increasingly using digital project management platforms that can simulate resource profiles, making levelling optimization an essential component of integrated project planning.

Resource levelling also interacts with risk management. Peaks in resource usage often coincide with increased risk of delays, accidents, and quality issues due to over-concentration of workforce or machinery. By spreading resources more evenly, managers can enhance safety and maintain consistent supervision levels.

The objective function f defined earlier serves as the evaluation metric for optimization algorithms. In a metaheuristic context, each candidate solution (chromosome in GA, particle in PSO, ant path in ACO) represents a possible scheduling and resource allocation configuration. The fitness of each candidate is evaluated using f, and the algorithm iteratively improves solutions through evolutionary or swarm dynamics. Within a hyper-heuristic framework like WHH, the objective function also guides higher-level decision-making. The controller evaluates how well each underlying heuristic performs based on the current fitness landscape and selects or combines them adaptively. This transforms the problem from simple search optimization to learning-based control, where the algorithm effectively learns to schedule the schedulers. Because the objective is multi-objective and nonlinear, the hyper-heuristic can employ reinforcement learning to balance exploitation (refining current reasonable solutions) and exploration (testing new strategies). Over iterations, the controller identifies which heuristic performs better under high fluctuation, high congestion, or convergence stagnation, ensuring that resource usage is dynamically optimized as the search progresses.

The WHH algorithm is a hybrid optimization framework that integrates RL with multiple metaheuristic strategies to achieve adaptive and self-regulating optimization performance. Unlike conventional metaheuristics that rely on a fixed search paradigm, WHH introduces a higher-level decision-making layer, the hyper-heuristic controller, which dynamically selects the most appropriate search operator or algorithm based on observed performance at each iteration.

The core philosophy behind WHH is analogous to how decision-making evolves in complex adaptive systems. Instead of committing to a single optimization paradigm (e.g., swarm-based or evolutionary), WHH continuously monitors the search dynamics and learns which metaheuristic performs best in the current landscape of the solution space. Through reinforcement learning, the controller maintains a balance between exploration, which encourages diversity to escape local optima, and exploitation, which focuses on refining promising solutions.

In practice, each metaheuristic within WHH contributes a unique search behavior. GA encourages global exploration through recombination and mutation; PSO provides convergence-driven swarm dynamics; ACO adds collective path reinforcement; SA allows probabilistic acceptance of inferior solutions to overcome local traps; and ICA models socio-political evolution, fostering competitive exploitation. The combination of these diverse behaviors, orchestrated by an RL-based control policy, enables WHH to adaptively shift between exploration and intensification in response to real-time feedback from the optimization environment.

The WHH algorithm is composed of two hierarchical layers:

I. Low-level layer (metaheuristics pool): this layer contains a set of metaheuristic algorithms, each with its own operators and control parameters. These algorithms act as the "actions" available to the reinforcement learning agent. At any iteration, the RL agent can select one of these metaheuristics to guide the evolution of solutions.

II. High-level layer (reinforcement learning controller): the RL controller observes the performance outcomes of previously selected algorithms and updates a value function or Q-table that estimates the expected reward for each metaheuristic. The reward typically corresponds to an improvement in the objective function, a reduction in constraint violations, or a combination of both.

The agent follows a mixed selection strategy that combines ε-greedy exploration and roulette-wheel selection. During exploration (with probability ε), the controller randomly selects a metaheuristic to maintain diversity. During exploitation (with probability 1−ε), it selects the algorithm with the highest expected reward, biasing the search toward the most effective strategy at that stage.

Each iteration proceeds as follows: the controller chooses a metaheuristic, applies it to the current population, evaluates the resulting solutions, and computes a reward based on the degree of improvement. The Q-values are then updated using the reinforcement learning update rule:

Q(at) ← Q(at) + α[rt + γmax Q(a) − Q(at)],

where Q(at) is the expected reward of action at (selected metaheuristic), rt is the observed improvement in fitness, α is the learning rate, and γ is the discount factor controlling the influence of future rewards.

The adaptive learning process enables WHH to gradually identify which metaheuristic performs better at different stages of the search. For example, GA or PSO might dominate in early stages to explore the global landscape, while SA or ICA might be favored during the late stages for local refinement and convergence.

The operation of the WHH algorithm follows a structured workflow that ensures a dynamic balance between global and local search capabilities. The workflow can be described as follows:

I. Initialization: the algorithm begins by generating an initial population of candidate solutions, typically represented as sequences of construction activities or task-resource assignments. Each solution encodes a potential schedule satisfying precedence relationships and resource constraints.

II. Evaluation: for each candidate solution, the fitness value is calculated based on the joint objective function that integrates project duration, resource fluctuation (Mx), and utilization distribution (My). This ensures that both temporal efficiency and resource stability are considered simultaneously.

III. Reward assignment: after applying a selected metaheuristic, the performance of the newly generated solutions is compared with that of the previous iteration. The reward function is computed as the difference in the multi-objective score before and after the update. Positive improvement yields higher rewards, reinforcing the chosen metaheuristic, whereas stagnation or deterioration leads to a penalty.

IV. Strategy selection: the reinforcement learning policy then determines the next metaheuristic to apply. The policy combines ε-greedy selection for exploration and roulette-wheel probability distribution for exploitation. This hybrid policy ensures that WHH avoids premature convergence while still favoring consistently performing strategies.

V. Population update: the selected metaheuristic modifies the population according to its own operators:

− GA: applies selection, crossover, and mutation to generate offspring.

− PSO: updates particle velocities and positions based on individual and collective experience.

− ACO: updates pheromone trails and constructs new solutions through probabilistic transitions.

− SA: perturbs the current solution and accepts new states according to a decreasing temperature schedule. − ICA: models imperialist assimilation and competition to refine the population toward stronger empires.

The updated population replaces the previous one based on fitness ranking and elitism preservation.

VI. Termination: the iterative process continues until the maximum number of iterations is reached or the improvement rate falls below a predefined convergence threshold. The best solution found is reported as the optimal or near-optimal construction schedule with balanced resource allocation and levelling.

The strength of the WHH algorithm lies in its adaptability, robustness, and generalization capability across diverse optimization problems. Traditional metaheuristics require manual tuning and perform inconsistently across different problem instances. In contrast, WHH autonomously learns which algorithm or operator is best suited for each stage of the search, reducing dependency on expert knowledge or parameter tuning. Moreover, the use of a reinforcement learning controller enables the algorithm to dynamically respond to changes in the problem landscape, such as constraint tightening, resource fluctuations, or new task dependencies, making it particularly suitable for real-world construction projects, which often involve uncertainty and dynamic conditions.

The WHH framework also facilitates parallelization and scalability. Each metaheuristic can be executed on separate computational threads or clusters, and the RL controller aggregates their performance statistics to make global decisions. This distributed architecture can significantly reduce computation time for large-scale scheduling problems.

Finally, by integrating diverse search paradigms (evolutionary, swarm-based, physics-inspired, and socio-political)WHH maintains both search diversity and intensification, ensuring that no single algorithmic bias dominates the optimization process. This combination of reinforcement learning and metaheuristic synergy positions WHH as a next-generation optimizer capable of addressing multi-objective, stochastic, and large-scale construction scheduling problems with high efficiency and stability.

The first set of experiments evaluates how effectively each algorithm can smooth resource consumption over the project timeline while maintaining an acceptable duration. Table 1 summarizes the main findings.

The results demonstrate a clear improvement in the smoothness of resource usage after optimization. The unoptimized baseline exhibits extreme fluctuations, with significant peaks indicating overloaded resource utilization and deep valleys of idle capacity. Among the baseline algorithms, ACO and ICA achieve moderate levelling improvements through their collective search and competitive mechanisms, respectively.

The proposed WHH algorithm, however, achieves the lowest fluctuation index (Mx = 950) and the smallest utilization variance (My = 11000), corresponding to a smoother, more balanced profile across the project horizon. The reduction of by more than 60 % compared to the unlevelled schedule and by ~20 % relative to the next-best algorithm (ICA), illustrating WHH’s superior capability to reduce both the intensity and the irregularity of resource demand.

Qualitatively, the resource histogram before and after WHH optimization shows a dramatic decline in peak values and a much flatter overall curve, signifying that manpower and equipment requirements are better distributed over time. This balanced profile implies lower hiring/firing cycles, fewer idle days, and more stable site operations.

Beyond levelling quality, the convergence behavior and consistency of each algorithm were assessed using the average fitness, standard deviation, and number of iterations to convergence. These results are summarized in Table 2.

The proposed WHH achieved the lowest mean fitness value (0.812), representing the most favorable trade-off among project duration, fluctuation, and utilization. Its standard deviation (0.018) is the smallest of all methods, revealing excellent run-to-run stability. WHH’s convergence rate, 47 iterations on average, is approximately twice as fast as GA and significantly faster than PSO, ACO, and SA.

This accelerated convergence results from the adaptive reinforcement-learning mechanism: the controller rapidly identifies which metaheuristics are most effective in the current search landscape and allocates computational effort accordingly. Early in the optimization, WHH tends to favor exploration-oriented algorithms (PSO and ACO), whereas later stages transition to exploitative algorithms (GA, SA, and ICA) for refinement. This self-adaptive orchestration ensures that search diversity is preserved without sacrificing convergence efficiency.

To determine whether the performance improvements offered by WHH are statistically significant, the Wilcoxon signed-rank test was conducted comparing WHH with each competing algorithm across 30 independent runs. The results are listed in Table 3.

All p-values are below 0.05, confirming that WHH’s improvements in fitness and convergence speed are statistically significant compared to every baseline algorithm. These results strengthen the claim that WHH’s learning-driven adaptability produces genuinely superior performance rather than random variation.

The following visual analyses illustrate WHH’s advantages more intuitively.

The resource histogram compares total resource usage before and after WHH optimization (Fig. 1). The pre-optimization curve shows sharp peaks at certain time intervals, indicating resource congestion. After optimization, the curve becomes noticeably flatter, confirming reduced variability and smoother workforce deployment.

The convergence curves plot the average fitness value across iterations for GA, PSO, and WHH (Fig. 2). While GA and PSO show early progress followed by stagnation, WHH achieves a consistently steeper descent, reaching optimal fitness in fewer than 50 iterations. The smooth slope reflects stable learning behavior and balanced exploration–exploitation control.